I think even if a dwarf woman had only a cottony textured beard, as I said before, most of the other races wouldn't distinguish.

But Tolkien goes beyond this with his Dwarves in my opinion. Yes some men can be mistaken for women simply due to long hair, due to an expectation within a given culture, but that doesn't mean these men cannot be told apart from their women in other ways of course -- but Tolkien's Dwarf-women are indistinguishable from the Dwarf-men, excepting that they go not to war and seldom leave their halls and bowers.

Again, I think we can see into Tolkien's mind here with the Iluvatar example: Aule had made male Dwarves, Iluvatar therefore kept his design so much so that other peoples could not tell male from female apart -- so appearance includes beards, yes, but is not limited to beards, and thus I think not limited to simply being fooled by a woman with a beard.

Jackson's Dwarf-women are a perfect example to my mind -- they look like women with beards. But if that's what Tolkien had in mind why include voice, and even gait, and appearance in general? He could have easily written that Dwarf-women were sometimes mistaken for Dwarf-men because they were bearded, and that would leave the impression you seem to be describing...

... but Tolkien's Dwarf-women sound like Dwarf-men and even walk like Dwarf-men, and they look like Dwarf-men in general [not simply because they are bearded] so much that other races can't tell the difference. They might dress differently, but yet not if they travel in any case, so that won't work either... so along comes the false idea that there are no Dwarf-women.

'nor in any wise' can they be told apart [by other peoples] save that Dwarf-women go not to war and seldom leave their halls. To me that speaks to more than mistakes due to cultural expectations.